Noncausal IIR Fractional Hilbert Transformers With Equiripple or Flat Phase Response

Noncausal infinite impulse response (IIR) systems yield a much better approximation of desired response than causal systems of the same complexity. Today´s technology also enables their efficient implementation. In the design of Hilbert transformers, the noncausal approach has been exploited only for conventional transformers. This brief presents a method for the design of noncausal IIR fractional Hilbert transformers based on the elliptic approximation of the desired phase shift. All-pass transformers with equiripple and flat phase responses are considered. The method is given in closed form, which makes the design robust and suitable for high-order transformers.